Answers
Rewrite the second expression as
[tex]\dfrac1{1+x^m + x^{-n}} = \dfrac{x^{\ell+n}}{x^{\ell+n} + x^{\ell+m+n}+x^\ell} = \dfrac{x^{-m}}{x^{-m} + 1 + x^\ell}[/tex]
and the third expression as
[tex]\dfrac1{1 + x^n + x^{-\ell}} = \dfrac{x^\ell}{x^\ell + x^{\ell+n} + 1} = \dfrac{x^\ell}{x^\ell + x^{-m} + 1}[/tex]
so the fractions all have the same denominator.
Then combining the fractions gives the desired result,
[tex]\dfrac1{1+x^\ell+x^{-m}} + \dfrac1{1+x^m+x^{-n}} + \dfrac1{1+x^n+x^{-\ell}} = \dfrac{1+ x^\ell + x^{-m}}{1+x^\ell+x^{-m}} = \boxed{1}[/tex]
Related Questions
What is a table value in math?
Answers
To display the relationship between data objects, tables of values are utilized. In scientific class, you might employ a table of values.
what is sequence ?A group of numbers, often known as "terms," such as 2, 5, or 8, make up a sequence. Some sequences can be made infinitely long by utilizing a specific pattern that they follow. Add 3 and use the example of 2,5,8 to continue the series. There, you can find formulas that outline where to hunt for terms in a series. A collection of elements in some order is what is referred to as a sequence informally in mathematics (or events). Like a set, it is made up of parts (also called elements or terms). The entire, perhaps indefinite number of arranged objects is referred to as the length of the sequence. the process of logically ordering two or more objects. Chronological.
given
To display the relationship between data objects, tables of values are utilized. In scientific class, you might employ a table of values. Researchers and scientists record their data using tables of numbers, then examine the data to look for patterns.
This pattern can then be applied to generate forecasts.
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Darla is able to drive her car 37.5 miles per gallon of gasoline. Write an inequality that could be used to determine the minimum number of gallons, g, of gasoline Darla would need to drive 120 miles to her brother’s house.
i need help
Answers
The inequality can be written as g * 37.5 >= 120.
What is linear inequality?
A linear inequality is a mathematical statement that describes a relationship between two or more variables that form a half-plane when graphed. The equation of a linear inequality is in the form of "ax + by < c" or "ax + by > c" or "ax + by <= c" or "ax + by >= c", where x and y are variables, and a, b and c are constants.
An inequality that could be used to determine the minimum number of gallons, g, of gasoline Darla would need to drive 120 miles to her brother's house is:
g >= 120/37.5
This inequality states that the number of gallons, g, must be greater than or equal to the number of miles Darla needs to drive, 120, divided by the number of miles per gallon her car gets, 37.5. This is because Darla wants to ensure that she has enough gasoline to make the trip, and she may not want to risk running out of gas on the way.
Another way to write this inequality is
g * 37.5 >= 120
This inequality represents the same meaning as before, we multiply g by the number of miles per gallon the car gets, 37.5 and it should be greater than or equal to the distance she needs to travel which is 120 miles.
Hence, the inequality can be written as g * 37.5 >= 120.
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Which value could be substituted for the variable to make the equation TRUE? 21 = t - 7
Answers
Answer:
4 or t = -8
Step-by-step explanation:
Answer:
Step-by-step explanation:
You are solving for the variable, t. Note the equal sign, what you do to one side, you do to the other.
To isolate t, add 7 to both sides of the equation:
21 = t - 7
21 (+7) = t - 7 (+7)
21 + 7 = t
t = 28
t = 28 is your answer.
Check: Plug in 28 for t in the given equation:
21 = t - 7
21 = (28) - 7
21 = 21 (True).
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is there a proportional relationship between the original price of an item and it’s sale price?
Answers
Answer:
It seems that your question is missing something, it looks like a question to a previous question. Please add all info when making a question. Also you can comment underneath my reply with that additional info.
Given that k(3) = 0 and h(- 4) = 0, for the polynomial h(x)=x^4+2x^3-13x^2-14x+24
Write h(x) in factored form and write down all the real roots of the polynomial.
Answers
The polynomial h(x)=x^4+2x^3-13x^2-14x+24 in the factored form is (x−1)(x+2)(x−3)(x+4). The real roots of the polynomial is x= 1, x = 3, x = -2, x = -4.
What is a polynomial function?
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
The polynomial function is -
h(x)=x^4+2x^3-13x^2-14x+24
Divide the polynomial h(x) by (x-1) -
(x^4+2x^3−13x^2−14^x+24)=(x−1)(x3+3x2−10x−24)
Divide (x^3+3x^2−10x−24) by (x+2) -
(x−1)(x^3+3x^2−10x−24)=(x−1)(x+2)(x^2+x−12)
Solve the quadratic equation x^2+x−12=0.
x^2+x−12=0
x^2+4x-3x-12=0
x(x+4)-3(x+4)=0
(x+4)(x-3)=0
So, (x−1)(x+2)(x^2+x−12)=(x−1)(x+2)(x−3)(x+4)
Therefore, x^4+2x^3−13x^2−14x+24=(x−3)(x−1)(x+2)(x+4) .
The Rational Root Theorem tells us that if the polynomial has a rational zero then it must be a fraction q/p, where p is a factor of the constant term and q is a factor of the leading coefficient.
We can see that p(1)=0 so x=1 is a root of a polynomial h(x).
Divide the polynomial by (x-1) -
(x^4+2x^3−13x^2−14x+24)/(x-1)=(x^3+3x^2−10x−24)
Divide (x^3+3x^2−10x−24) by (x-3) -
(x^3+3x^2−10x−24)/(x-3) = (x^2+6x+8)
To find the last zero, solve equation x+4=0
x=-4
Therefore, the real roots are - x = 1, 3, -2, -4.
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What are function answers?
Answers
An equation that has one solution for y for each value of x is referred to be a function. A function pairs each input of a particular type with exactly one output.
what are functions ?The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
An equation that has one solution for y for each value of x is referred to be a function.
A function pairs each input of a particular type with exactly one output. Instead of y, it is typical to name functions f(x) or g(x). f(2) instructs us to calculate the value of our function when x is equal to 2.
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An investor invested a total of $1,600 in two mutual funds. One fund earned a 9% profit while the other earned a 4% profit. If the investor's total profit was $84, how much was invested in each mutual fund?
Answers
The amount invested in each mutual fund is $400 and $1200 respectively
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 10 and 8x − 4y = 2
Let represent the amount the first fund get by x and the amount the second fund get by y.
Therefore x+y = 1600 equation 1
and 9/100 × x + 4/100 × y = 84
9x/100 + 4x/100 = 84
multiply through by 100
9x + 4x = 8400 equation 2
using elimination method
9x+ 9y = 14400 equation 3
9x + 4y = 8400 equation 4
subtract equation 4 from 3
5y = 6000
divide both sides by 5
y = 6000/5
y = $1200
substitute 1200 for y in equation 1
1200+x = 1600
x = 1600-1200
x = 400
Therefore the first fund will get $400 and the second fund will get $1200
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A new cyclindrical swimming pool is being built at the local rec center. It has a radius of 13 feet and a height of 6 feet. Tim determined that 1,014Pi ft3 of water would be needed to fill the pool, but jasmine calculated that 3,185.57 ft3 of water would be needed. Explain who calculated the volume properly.
Answers
Answer:
:Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded
Step-by-step explanation:
Answer: Both Tim and Jasmine calculated the volume properly. Tim gave the exact answer with pi in it, whereas Jasmine multiplied by pi and then rounded to the nearest hundreth.
Step-by-step explanation:
Use the graph to find the unit rate.
Answers
On solving the question, unit rate by using the given graph could be 2.4 potatoes/pound
What is a graph ?Graph can be defined as the visual representation which is used to represent the data.
The unit rate is the slope of the line.
The slope of the line = (change in y-value)/(change in x-value)
= (36 potatoes - 12 potatoes)/(15 pounds - 5 pounds)
= (24potatoes)/(10 pounds)
= 2.4 potatoes/pound
The relationship here is proportional, so the line goes through the point (0, 0) and the unit rate can be figured from any point:
(12 potates)/(5 pounds)
= (24 potatoes)/(10 pounds)
= (36 potatoes)/(15 pounds) = 2.4 potatoes/pound
Hence, The unit rate by using the given graph could be 2.4 potatoes/pound .
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The correct question is -
Identify the unit rate in the graph.
A. 40mph
B. 75mph
C. 50mph
D. 25mph
Which number is greater than the number at point P?
Answers
The correct answer is -60
Why did we choose -60 not -70?When you look at -70 it looks like it would be higher then -60 but -60 is actually higher then -70 because it has a negative line.
Therefore, the correct answer is -60
Is the set of 2nd coordinates?
Answers
No, the set of 2nd coordinates is not a set. It is a pair of numbers that identifies a particular point on a coordinate plane.
1. It is not a collection of items.
2. It is not an ordered list.
3. It is not a group of elements.
4. It is not a set of elements.
5. It is not a collection of points.
6. It is not a grouping of numbers.
7. It is not a sequence of numbers.
8. It is not a selection of numbers.
9. It is not a combination of numbers.
10. It is not a union of numbers.
11. It is not a cluster of numbers.
12. It is not a set of components.
13. It is not a combination of values.
14. It is not a sequence of values.
15. It is not a selection of values.
16. It is not a union of values.
17. It is not a set of points.
18. It is not a set of data points.
19. It is not a selection of coordinates.
20. It is not a set of ordered pairs.
21. It is not a set of numbers.
22. It is not a set of measurements.
23. It is not a set of data.
24. It is not a set of variables.
25. It is not a set of parameters.
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What is the difference between ABC and XYZ?
Answers
Therefore , the solution of the given problem of triangle comes out to be the planning elements are simultaneously given a class designation from ABC or XYZ during the analysis.
Describe the triangle.Since a triangle has three sides or three vertices, it is a polygon. It is a fundamental geometric shape. Triangle ABC is the moniker given to one of a triangle that has endpoints A, B, and C. When the points are not collinear, a singular plane and triangle are found in Euclidean geometry. A triangle is a polygon if it has three sections and three corners. The points where its three sides meet are known as the triangle's corners. The product of three triangle angles is 180 degrees.
Here,
Using the ABC/XYZ technique, planned units (characteristic product combinations, SKUs) are grouped according to their value (income or product sales) and consumption or sales dynamics.
The planning elements are simultaneously given a class designation from ABC or XYZ during the analysis.
Therefore , the solution of the given problem of triangle comes out to be the planning elements are simultaneously given a class designation from ABC or XYZ during the analysis.
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A triangle has sides with lengths of 32 kilometers, 60 kilometers, and 68 kilometers. Is it a right triangle?
Answers
Answer:
yes
Step-by-step explanation:
a^2 + b^2 = c^2
so
32^2 + 60^2 = 68^2
1024 + 3600 = 4624
Mr. Jakarta is having a well built in his backyard. On Monday 175 feet of the well was drug, and another 165 feet was dug tuesday. How many feet deep was well dug relative to ground level
Answers
340 feet deep was well dug relative to ground level
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Mr. Jakarta is having a well built in his backyard.
On Monday 175 feet of the well was drug
Another 165 feet was dug tuesday.
We need to find the how many feet deep was well dug relative to ground level
To find the number of feet, we simply make an addition of the number of feet dug on both days
The total will be 175 feet + 165 feet = 340 feet
Hence, 340 feet deep was well dug relative to ground level
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ANSWER NUMBER FIVE ONLY! WHOEVEER GIVES RIGHT ANSWER WILL GET BRAINLEST PLEASE HELP
5. The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is a₁, which is an
equation for the nth term of this sequence?
1) a = 8m+10
2) a = 8n - 14
3) a = 16n+10
4) a, = 16n-38
Answers
The equation for the nth term of this sequence is [tex]a_{n}[/tex] = 8n - 14. The solution has been obtained by using the concept of arithmetic progression.
What is arithmetic progression?
The difference between any two consecutive integers in an arithmetic progression (AP) sequence of numbers is always the same amount. It also goes by the name Arithmetic Sequence.
We are given that the third term is 10.
This means that [tex]a_{3} =10[/tex]
So, n=3
Substituting this value in the given equations, we get
1) [tex]a_{n}[/tex] = 8*3+10 = 34
2) [tex]a_{n}[/tex] = 8*3 - 14 = 10
3) [tex]a_{n}[/tex] = 16*3+10 = 58
4) [tex]a_{n}[/tex] = 16*3 - 38 = 10
So, the second and the fourth equation satisfy the condition.
We are also given that the fifth term is 26.
This means that [tex]a_{5} =26[/tex]
So, n=5
Substituting this value in the given equations, we get
2) [tex]a_{n}[/tex] = 8*5-14 = 26
4) [tex]a_{n}[/tex] = 16*5 - 38 = 42
So, the second equation satisfies the condition.
Hence,the equation for the nth term of this sequence is [tex]a_{n}[/tex] = 8n - 14.
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Which statement is modeled by the expression? 100p Responses The coach received 100 tokens for the amusement park rides. If there are p players on the team, each player will receive 100p tokens. The coach received 100 tokens for the amusement park rides. If there are , p, players on the team, each player will receive , 100 over p, , tokens. After the league had supplied each player with a uniform, there were 100 uniforms left over. If there are p players in the league, 100p is the number of uniforms the league had originally. After the league had supplied each player with a uniform, there were 100 uniforms left over. If there are , p, players in the league, , 100 over p, is the number of uniforms the league had originally. One hundred more players signed up for soccer than the league had planned for. The league had p uniforms in stock. The number of uniforms the league needs to buy to make up the difference is 100p. One hundred more players signed up for soccer than the league had planned for. The league had p uniforms in stock. The number of uniforms the league needs to buy to make up the difference is 100 over p ., Each player in the league was given 100 tickets to sell. If there are p players in the league, the total number of tickets to sell is 100p Each player in the league was given 100 tickets to sell. If there are , p, players in the league, the total number of tickets to sell is , 100 over p
Answers
"100p" is: "If there are p players on the team, each player will receive 100p tokens." Have a good day
Rider complete 160 lap the race to complete the race. With each lap meauring 0. 25km. If a ride ha already cylcled 4. 75km how many lap doe he have left to finih the race
Answers
The rider has 141 laps left to finish the race.
If a rider has already cycled 4.75 km, and each lap measures 0.25 km, we can determine how many laps the rider has completed by dividing the distance already cycled by the distance per lap.
To find out how many laps the rider has left to finish the race, we will use the information on the total number of laps to complete the race: 160 laps.
The rider has completed:
4.75 km / 0.25 km = 19 laps
The rider has yet to finish:
160 laps - 19 laps = 141 laps
So the rider has 141 laps left to finish the race.
Therefore, the rider has 141 laps left to finish the race.
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Can the length 4.5 cm 3.5 cm 6.4 cm be the dimensions of a triangle?
Answers
The length 4.5 cm 3.5 cm 6.4 cm can be the dimensions of a triangle according to rule.
Considering the dimensions of triangle, the one side of the triangle should be less than the sum of other two sides. Based on the rule, let us say that 4.5, 3.5 and 6.4 cm is side a, b and c.
Keep the values to compare the sides
Side a + side b > side c
4.3 + 3.5 > 6.4
Add the digits
7.8 > 6.4
Side b + side c > side a
3.5 + 6.4 > 4.5
Add the digits
9.9 > 4.5
side c + side a > side b
6.4 + 4.5 > 3.5
Add the digits
10.9 > 3.5
All the sides follow the rule. Therefore, the mentioned lengths are possible for a triangle.
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Rectangle is similar to rectangle . Which proportion can be used to find the value of x?
Answers
If rectangle is similarity to rectangle, to find the value of x we use proportion (c) 5/12 = 2/x.
What is called similarity of shapes?When applying a scale factor, similar shapes are enlarged versions of one another.
All of the matching angles and lengths in related shapes are equal and in the same ratio.
If two figures share the same shape, congruent corresponding angles (which means the angles in the same places of each shape are the same), and identical scale factors, they are said to be "similar figures."
Given that rectangle EFGH is similar to rectangle JKLM, it means the corresponding sides of both rectangles are similar, and as such the ratios if the corresponding sides of rectangle EFGH and rectangle JKLM would be equal.
Thus, EF/JK = FG/KL
Since, EF = 5; JK = 12; FG = 2; and KL= x, therefore, the proportion to use in finding x would be:
5/12= 2/x
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Solve for X and find the measure of the angle indicated in bold.
for the ones that doesn't have a number then the first one is 25, 27
Also please help. I need to get this done by tomorrow. please also explain how you got the answers two for everyone of the problems, thanks!
Answers
Due to the corresponding angle property, which requires that the sum of neighboring opposite angles be 180, the angles are 90 and 79.8.
what is angle ?In Euclidean geometry, an angle is a shape that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to form an angle in the plane where they are positioned. When two planes collide, an angle is also created. They are referred to as dihedral angles. An angle in plane geometry is the possible configuration of two rays or lines that share a termination. The origin of the English term "angle" is the Latin word "angulus," which meaning "horn." The vertex is the point where the two rays, also known as the sides of the angle, converge.
given
Due to the property of matching angles,
the angles are 90 and 21x + 8
90 + 21x + 18 = 180
= 108 + 21x = 180
= 21x = 72
x = 3.42
Due to the corresponding angle property, which requires that the sum of neighboring opposite angles be 180, the angles are 90 and 79.8.
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A phone case is 10 times cheaper than the phone. Herman paid 660 for his phone and case. What was the cost of the phone and what was the cost of the phone case
Answers
Answer:
Let x be the cost of the phone.
we know that the cost of the phone case is 10 times cheaper than the phone so the cost of the case is x/10
We also know that the total cost of the phone and the case is 660.
so we can write an equation:
x + (x/10) = 660
We can solve this equation for x by multiplying both sides by 10:
10x + x = 6600
11x = 6600
x = 600
So the cost of the phone is 600 and the cost of the phone case is 600/10 = 60
Solve the perimeter of this shape
Answers
The perimeters of the two composite figures are listed below:
Case C: 50.913π mm
Case D: 20.310 cm
How to determine the perimeter of a composite figure
In this problem we find two composite figures, whose perimeter have to be found. Perimeter is the length of all borders of the figure. The first figure is formed two semicircles and the second figure is formed by two semicircles and two right triangles, whose perimeter formulas are:
Semicircle
s = π · r
Triangle
s = b + h + p
Where:
r - Radius, in length unit.b - Width, in length unit.h - Height, in length unit.p - Hypotenuse, in length unit.Case c - The perimeter of the shape is:
s = π · (28 mm) + π · (14 mm) + 28 mm
s = 50.913π mm
Case d - The perimeter of the shape is:
s = 2π · (1.8 cm) + 2 · (4.5 cm)
s = 20.310 cm
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Smith and Frank thought of the same number. They multiplied the number by 5 and then increased the product by 5 for a final result of -80. Of what number were they thinking?
Answers
Answer
-17
Step-by-step explanation:
5 times -17= -85 and then add 5 = -80
A soft drink is available in two packs - (i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and (ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?
Answers
Answer: To find the capacity of the tin can, we can use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length is 5 cm, the width is 4 cm, and the height is 15 cm. So the volume of the tin can is 5 x 4 x 15 = 300 cubic cm.
To find the capacity of the plastic cylinder, we can use the formula for the volume of a cylinder, which is pi x radius squared x height. The diameter of the circular base is 7 cm, so the radius is half of that, or 3.5 cm. So the volume of the plastic cylinder is pi x (3.5 cm)^2 x 10 cm = 385.4 cubic cm.
So the plastic cylinder has a greater capacity by 385.4 - 300 = 85.4 cubic cm.
Step-by-step explanation:
find the sum of: (-14.2b - 97.35) + (6.76d - 118.7 - 3.4d )
Answers
The sum of: (-14.2b - 97.35) + (6.76d - 118.7 - 3.4d ) is -14.2b + 3.36d -216.05
How to determine the sum?From the question, we have the following parameters that can be used in our computation:
(-14.2b - 97.35) + (6.76d - 118.7 - 3.4d )
Remove the brackets
So, we have
-14.2b - 97.35 + 6.76d - 118.7 - 3.4d
Evaluate the like terms
-14.2b + 3.36d -216.05
Hence, the sum is -14.2b + 3.36d -216.05
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the premiter of a rectangle is the some of the lengths and its four sides which expression where1=length and w = width does not show this relationship
Answers
Answer: The perimeter of a rectangle is the sum of the lengths of its four sides which is given by the expression: P = 2l + 2w (where l is the length and w is the width)
The expression that does not show this relationship is P = l + w
It doesn't show the relationship because it doesn't take into account the two sides that are equal to the width and the two sides that are equal to the length.
P = 2l + 2w shows the relationship as it considers both length and width of the rectangle twice, once for each pair of sides.
Step-by-step explanation:
Question Find the distance between the points E(3, 7) and F(6, 5).
Answers
The distance between the points E(3, 7) and F(6, 5) is 3.605 units.
What is Distance Formula?Algebraic expression that gives the distances between pairs of points in terms of their coordinates.
The distance between two points having coordinates P(a, b) and Q(c, d) is,
D= √(c-a)² + (b-d)².
Given:
Points E(3, 7) and F(6, 5).
Now, using Distance Formula
D= √(6-3)² + (5-7)²
D = √(3)² + (2)²
D= √9+4
D= √13 units
D= 3.605 unit
Hence, the distance is 3.605.
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Which relation is a function?
A.
B.
C.
Answers
Answer:
Function A
Step-by-step explanation:
doesn't have vertical points
Read the scenario and select a correct option for Part 1-3 questions.
Afnan has 24 coins in his pocket. They are all quarters and dimes and their total value is $4.65.
Part 1: What is the system of equations that represents this situation?
Part 2: How many dimes does he have?
Part 3: How many quarters does he have?
Answers
The system of equations that represents this situation is D + Q =24 and 10D + 25Q = 465 with 15 and 9 quarters and dimes respectively.
What are dimes?The dime is a ten-cent coin that is one-tenth of a dollar and is officially known as "one dime" in American use. The Coinage Act of 1792 initially allowed this denomination.The dime is the smallest and thinnest denomination now in circulation in the United States.Its obverse has President Franklin D. Roosevelt's profile, while its reverse features, from left to right, an olive branch, a torch, and an oak branch.The dime is the only currency in general circulation in the United States that is not valued in terms of dollars or cents. The cost to make a dime in 2011 was 5.65 cents.Given that
let the quarter be represented by Q and dimes with D
D + Q =24 (multiply this by 10)
10D + 10Q = 240
10D + 25Q = 465
Subtracting both the equations:
15Q =225
Q = 225/15 = 15 quarters
Now putting this value in equation 1st we get
D = 24-15 = 9 dimes
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What does 2 exponent mean?
Answers
Exponent 2 means the number of times one number is multiplied. The number of time the base is multiplied.
The Exponents refers to the repeated multiplication of the same thing by itself.
For example, [tex]x^{2}[/tex] . here 2 is the exponent and x is the base. Then we can write it as x . x . The base is multiplied by 2 time by itself.
Exponents are also called powers or orders. This is the shorthand for repeated multiplication of the same thing by itself. This process of using exponents is called "raising to a power" where the exponent is the "power". The expression [tex]4^{3}[/tex] is pronounced as four raised to the third power", "four, raised to the power three", or "four to the third". It stands for many times the value is being multiplied.
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